Search Results for "bridges-from-classical-to-nonmonotonic-logic"

Bridges from Classical to Nonmonotonic Logic

Bridges from Classical to Nonmonotonic Logic

  • Author: David Makinson
  • Publisher: College Publications
  • ISBN: 9781904987000
  • Category: Computers
  • Page: 216
  • View: 4549
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Imagine a robot trying to size up a difficult situation, to find a way of responding. Its sensors receive streams of information from which it tries to reach judgements. If it relies on deduction alone, it will not get far, no matter how fast its inference engines; for even the most massive information is still typically incomplete: there are relevant issues that it does not resolve one way or the other. The robot, or human agent for that matter, needs to go beyond these limits. It needs to `go supraclassical', inferring more than is authorised by classical logic alone. But such inferences are inherently uncertain. They are also nonmonotonic, in the sense that the acquisition of further information, even when consistent with the existing stock, may lead us to abondon as well as add conclusions. Nonmonotonic logic is the study of such reasoning and has been the subject of intensive research for more than two decades. But for the newcomer it is still a disconcerting affair, lacking unity with many systems going in different directions. The purpose of this book is to take the mystery out of the subject, giving a clear overall picture of what is going on. It makes the essential ideas and main approaches to nonmonotonic logic accessible, and meaningful, to anyone with a few basic tools of discrete mathematics and a minimal background in classical propositional logic. It is written as a textbook, with detailed explanations, examples, comments, exercises and answers. Students and instructors alike will find it an invaluable guide.

The Many Valued and Nonmonotonic Turn in Logic

The Many Valued and Nonmonotonic Turn in Logic

  • Author: Dov M. Gabbay,John Woods
  • Publisher: Elsevier
  • ISBN: 9780080549392
  • Category: Mathematics
  • Page: 690
  • View: 7578
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The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence. The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called “left non-monotonicity , it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called “right non-monotonicity , limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained. In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs. The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. Detailed and comprehensive chapters covering the entire range of modal logic. Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.

Logics in Artificial Intelligence

Logics in Artificial Intelligence

10th European Conference, JELIA 2006, Liverpool, UK, September 13-15, 2006, Proceedings

  • Author: Michael Fisher,Wiebe van der Hoek,Boris Konev,Alexei Lisitsa
  • Publisher: Springer Science & Business Media
  • ISBN: 354039625X
  • Category: Computers
  • Page: 516
  • View: 4576
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Logics provide a formal basis, and key descriptive notation, for the study and dev- opment of applications and systems in Arti'cial Intelligence (AI). With the depth and maturity of formalisms, methodologies,and systems today, such logics are increasingly important. The European Conference on Logics in Arti'cial Intelligence (or Journees ́ Europeennes ́ sur la Logique en Intelligence Arti'cielle -- JELIA) began back in 1988, as a workshop, in response to the need for a European forum for the discussion of emerging work in this ?eld. Since then, JELIA has been organised biennially, with - glish as of'cial language, and with proceedings published in Springer's Lecture Notes in Arti'cial Intelligence. Previousmeetingstookplace in Roscoff,France(1988),Ams- ́ terdam,Netherlands(1990),Berlin,Germany(1992),York,UK (1994),Evora,Portugal (1996), Dagstuhl, Germany (1998), Malaga, ́ Spain (2000), Cosenza, Italy (2002), and Lisbon, Portugal (2004). The increasing interest in this forum, its international level with growing parti- pation from researchers outside Europe, and the overall technical quality, has turned JELIA into a major forum for the discussion of logic-based approaches to AI. JELIA 2006constitutedtheTenthInternationalConferenceonLogicsinArti'cial Intelligence, and was held in Liverpool (UK) in September 2006. As with previous JELIA conf- ences, the aim of JELIA 2006 was to bring together active researchers interested in all aspects concerning the use of logics in AI to discuss current research, results, problems and applications of both a theoretical and practical nature. We received a total of 96 submissions, comprising 77 regular papers and 19 tool - scriptions.

The Logic of Legal Requirements

The Logic of Legal Requirements

Essays on Defeasibility

  • Author: Jordi Ferrer Beltrán,Giovanni Battista Ratti
  • Publisher: Oxford University Press
  • ISBN: 0199661642
  • Category: Law
  • Page: 421
  • View: 9806
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Does the law contain implicit exceptions to its own rules? If so, what consequence does that have for understanding the relationship between law and morality? This collection gathers leading legal philosophers to analyse the logical structure of legal norms, advancing the understanding of the general philosophy of law.

The Bulletin of Symbolic Logic

The Bulletin of Symbolic Logic

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Logic, Symbolic and mathematical
  • Page: N.A
  • View: 3685
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Crítica

Crítica

revista hispanoamericana de filosofía

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Philosophy
  • Page: N.A
  • View: 5991
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Handbook of Philosophical Logic

Handbook of Philosophical Logic

  • Author: D.M. Gabbay,Franz Guenthner
  • Publisher: Springer Science & Business Media
  • ISBN: 9781402030918
  • Category: Philosophy
  • Page: 372
  • View: 9411
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The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications

Mathematical Reviews

Mathematical Reviews

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 8967
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The Haskell Road to Logic, Maths and Programming

The Haskell Road to Logic, Maths and Programming

  • Author: Kees Doets,Jan van Eijck,Jan Eijck
  • Publisher: Kings College Publications
  • ISBN: N.A
  • Category: Mathematics
  • Page: 426
  • View: 6691
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Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply There is no royal road to mathematics. Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book, the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others. This is the updated, expanded, and corrected second edition of a much-acclaimed textbook. Praise for the first edition: Doets and van Eijck s The Haskell Road to Logic, Maths and Programming is an astonishingly extensive and accessible textbook on logic, maths, and Haskell. Ralf Laemmel, Professor of Computer Science, University of Koblenz-Landau

Towards Mathematical Philosophy

Towards Mathematical Philosophy

Papers from the Studia Logica conference Trends in Logic IV

  • Author: David Makinson,Jacek Malinowski,Heinrich Wansing
  • Publisher: Springer Science & Business Media
  • ISBN: 1402090846
  • Category: Mathematics
  • Page: 344
  • View: 8898
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area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic.